Finite Group Databasebeta

← Group #512167

Character table — Group #512167

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122222224444444444444444888888884444448888888888884444444444444444161616161616161616161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ7111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-1
χ1011111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-11
χ1111111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11
χ1211111111-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1
χ1311111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11
χ1411111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-1
χ1611111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1-11
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ1822222222222222222222-2-2-2-200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ1922222222222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ20222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22222000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-222000000000000000000000000000022−2−2−2−22222−2−2−2−2220000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-20000000022-2-2220000000000000000000000000000−2−22222−2−2−2−22222−2−20000
χ2622222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002222-2-2000000000000000000000000000022−2−2−2−222−2−22222−2−20000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-2000000002222-2-20000000000000000000000000000−2−22222−2−222−2−2−2−2220000
χ292222-2-2-2-222-2-222-2-222-2-2000022−2−222−2−200000022−2−222−2−222−2−20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ302222-2-2-2-222-2-222-2-222-2-2000022−2−222−2−200000022−2−222−2−222−2−20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ312222-2-2-2-222-2-222-2-222-2-20000−2−222−2−222000000−2−222−2−222−2−2220000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ322222-2-2-2-222-2-222-2-222-2-20000−2−222−2−222000000−2−222−2−222−2−2220000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ332222-2-2-2-222-2-2-2-222-2-222000022−2−222−2−200000022−2−2−2−222−2−2220000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ342222-2-2-2-222-2-2-2-222-2-222000022−2−222−2−200000022−2−2−2−222−2−2220000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ352222-2-2-2-222-2-2-2-222-2-2220000−2−222−2−222000000−2−22222−2−222−2−20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ362222-2-2-2-222-2-2-2-222-2-2220000−2−222−2−222000000−2−22222−2−222−2−20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ372222-2-2-2-2-2-22222-2-2-2-222000022−2−222−2−2000000−2−22222−2−2−2−2220000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ382222-2-2-2-2-2-22222-2-2-2-222000022−2−222−2−2000000−2−22222−2−2−2−2220000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ392222-2-2-2-2-2-22222-2-2-2-2220000−2−222−2−22200000022−2−2−2−22222−2−20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ402222-2-2-2-2-2-22222-2-2-2-2220000−2−222−2−22200000022−2−2−2−22222−2−20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ412222-2-2-2-2-2-222-2-22222-2-2000022−2−222−2−2000000−2−222−2−22222−2−20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ422222-2-2-2-2-2-222-2-22222-2-2000022−2−222−2−2000000−2−222−2−22222−2−20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ432222-2-2-2-2-2-222-2-22222-2-20000−2−222−2−22200000022−2−222−2−2−2−2220000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ442222-2-2-2-2-2-222-2-22222-2-20000−2−222−2−22200000022−2−222−2−2−2−2220000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ4522-2-22-22-200002i−2i2i−2i000022-2-22-22-22-22-2002i−2i0000002i−2i2i−2i000000002i2i−2i−2i22-2-2000000000000000000000000
χ4622-2-22-22-200002i−2i2i−2i000022-2-22-22-22-22-2002i−2i0000002i−2i2i−2i00000000−2i−2i2i2i-2-222000000000000000000000000
χ4722-2-22-22-200002i−2i2i−2i000022-2-2-22-22-22-22002i−2i000000−2i2i−2i2i000022-2-2000000002i2i−2i−2i00000000000000000000
χ4822-2-22-22-200002i−2i2i−2i000022-2-2-22-22-22-22002i−2i000000−2i2i−2i2i0000-2-22200000000−2i−2i2i2i00000000000000000000
χ4922-2-22-22-20000−2i2i−2i2i000022-2-22-22-22-22-200−2i2i000000−2i2i−2i2i000000002i2i−2i−2i-2-222000000000000000000000000
χ5022-2-22-22-20000−2i2i−2i2i000022-2-22-22-22-22-200−2i2i000000−2i2i−2i2i00000000−2i−2i2i2i22-2-2000000000000000000000000
χ5122-2-22-22-20000−2i2i−2i2i000022-2-2-22-22-22-2200−2i2i0000002i−2i2i−2i000022-2-200000000−2i−2i2i2i00000000000000000000
χ5222-2-22-22-20000−2i2i−2i2i000022-2-2-22-22-22-2200−2i2i0000002i−2i2i−2i0000-2-222000000002i2i−2i−2i00000000000000000000
χ532-22-2-222-22i−2i2i−2i000000002-22-22-22-2-22-222i−2i00002i−2i2i−2i0000000000002-22-200002i−2i2i−2i00000000000000000000
χ542-22-2-222-22i−2i2i−2i000000002-22-22-22-2-22-222i−2i00002i−2i2i−2i000000000000-22-220000−2i2i−2i2i00000000000000000000
χ552-22-2-222-22i−2i2i−2i000000002-22-2-22-222-22-22i−2i0000−2i2i−2i2i000000002i−2i2i−2i00002-22-2000000000000000000000000
χ562-22-2-222-22i−2i2i−2i000000002-22-2-22-222-22-22i−2i0000−2i2i−2i2i00000000−2i2i−2i2i0000-22-22000000000000000000000000
χ572-22-2-222-2−2i2i−2i2i000000002-22-22-22-2-22-22−2i2i0000−2i2i−2i2i0000000000002-22-20000−2i2i−2i2i00000000000000000000
χ582-22-2-222-2−2i2i−2i2i000000002-22-22-22-2-22-22−2i2i0000−2i2i−2i2i000000000000-22-2200002i−2i2i−2i00000000000000000000
χ592-22-2-222-2−2i2i−2i2i000000002-22-2-22-222-22-2−2i2i00002i−2i2i−2i000000002i−2i2i−2i0000-22-22000000000000000000000000
χ602-22-2-222-2−2i2i−2i2i000000002-22-2-22-222-22-2−2i2i00002i−2i2i−2i00000000−2i2i−2i2i00002-22-2000000000000000000000000
χ612-2-22-2-222000000002-22-22-2-222222-2-2-2-200002-2000000002-22-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ622-2-22-2-222000000002-22-22-2-222222-2-2-2-200002-2000000002-22-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ632-2-22-2-222000000002-22-22-2-22-2-2-2-2222200002-200000000-22-22000000002-2-22-222-200000000000000000000
χ642-2-22-2-222000000002-22-22-2-22-2-2-2-2222200002-200000000-22-2200000000-222-22-2-2200000000000000000000
χ652-2-22-2-22200000000-22-222-2-222222-2-2-2-20000-2200000000-22-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ662-2-22-2-22200000000-22-222-2-222222-2-2-2-20000-2200000000-22-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ672-2-22-2-22200000000-22-222-2-22-2-2-2-222220000-22000000002-22-2000000002-2-222-2-2200000000000000000000
χ682-2-22-2-22200000000-22-222-2-22-2-2-2-222220000-22000000002-22-200000000-222-2-222-200000000000000000000
χ6944-4-44-44-400004i−4i4i−4i0000-4-4440000000000−4i4i00000000000000000000000000000000000000000000000000
χ7044-4-44-44-40000−4i4i−4i4i0000-4-44400000000004i−4i00000000000000000000000000000000000000000000000000
χ7144-4-4-44-4400004i−4i−4i4i0000000022−22−222222−22−222200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ7244-4-4-44-4400004i−4i−4i4i00000000−222222−22−222222−220000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ7344-4-4-44-440000−4i4i4i−4i0000000022−22−222222−22−22220000000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ7444-4-4-44-440000−4i4i4i−4i00000000−222222−22−222222−2200000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ754-44-44-4-444i−4i−4i4i00000000000022−22−2222−222222−220000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ764-44-44-4-444i−4i−4i4i000000000000−222222−2222−22−2222000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ774-44-44-4-44−4i4i4i−4i00000000000022−22−2222−222222−22000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ784-44-44-4-44−4i4i4i−4i000000000000−222222−2222−22−22220000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ794-44-4-444-44i−4i4i−4i00000000-44-4400000000−4i4i0000000000000000000000000000000000000000000000000000
χ804-44-4-444-4−4i4i−4i4i00000000-44-44000000004i−4i0000000000000000000000000000000000000000000000000000
χ814-4-4444-4-4000000004-4-4400002222−22−22−22−2222220000000000000022−22−2222000000000000000000000000000000000000
χ824-4-4444-4-4000000004-4-440000−22−2222222222−22−2200000000000000−222222−22000000000000000000000000000000000000
χ834-4-4444-4-400000000-444-400002222−22−22−22−22222200000000000000−222222−22000000000000000000000000000000000000
χ844-4-4444-4-400000000-444-40000−22−2222222222−22−220000000000000022−22−2222000000000000000000000000000000000000
χ854-4-44-4-444000000004-44-4-444-4000000000000-44000000000000000000000000000000000000000000000000
χ864-4-44-4-44400000000-44-44-444-40000000000004-4000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.